sentence-transformers How to use JALLAJ/5epo with sentence-transformers:
from sentence_transformers import SentenceTransformer
model = SentenceTransformer("JALLAJ/5epo")
sentences = [
"How many more requests can the proposed method handle effectively compared to the RMLSA-OFC method before performance declines, based on the data in Figure 6?",
"is a great challenge to synchronize the pulse trains, and this will induce extra interpulse jitter. Perfect repetition rate multiplication can be realized by the temporal Talbot or self-imaging effect through propagating a periodic temporal signal in a dispersive medium under the first-order dispersion conditions.25 Further, repetition rate demultiplication could also be realized by introducing a suitable periodic temporal phase modulation to the original signal and carefully controlling the amount of dispersion.26 However, both of these two schemes mentioned above require extra optical systems out of the laser cavities to modify the repetition rates of the pulse sources. They increase the system complexity and make these systems loose their attractiveness for portable and robust device operation. An intralaser cavity method is by harmonic mode-locking (HML), where the pulse energy is quantized by the peak-power-limiting effect. Generally, much higher pump power is needed for passive HML lasers to boost its repetition rates to tens of GHz.27,28 Both the intracavity noise fluctuation and the chance of the pulse drop in-out increase along with the increase of the harmonic order.,9,29 This prevents boosting the laser repetition rate beyond 100 GHz. Although pulse sources at repetition rates beyond $100\\ \\mathrm{GHz}$ can be realized by employing active HML schemes,3 a stable radio frequency source is needed and it restricts the dimension and cost for integration applications of the active HML lasers.",
"$$\nY=\\frac{\\gamma^{2}L^{2}}{\\theta}X^{3}-\\frac{2\\delta_{1}\\gamma L}{\\theta}X^{2}+\\frac{(\\delta_{1}^{2}+\\alpha^{2})}{\\theta}X.\n$$ \nwhere $Y=\\left|\\psi_{\\mathrm{in}}\\right|^{2}$ is the pump power, $X=\\left|\\psi\\right|^{2}$ is the intracavity power, ${\\alpha}=({\\alpha}_{0}L+\\theta)/2$ is the total loss per roundtrip. The turning points of the function $Y(X)$ can be calculated by setting the first derivative $d Y/d X$ to zero as \n$$\n3\\gamma^{2}L^{2}X^{2}-4\\delta_{1}\\gamma L X+(\\delta_{1}^{2}+\\alpha^{2})=0.\n$$ \nThe function $X(Y)$ given by Eq. (6) has a bistable region when Eq. (7) has two different real roots of $X.$ which requires $\\delta_{1}^{2}>3\\alpha^{2}$ . The two real roots corresponding to the two turning points of the bistable curve are given by \n$$\nX_{1,2}=\\frac{2\\delta_{1}\\pm\\sqrt{\\delta_{1}^{2}-3\\alpha^{2}}}{3\\gamma L}.\n$$",
"To compare the proposed method with widely used state-of-the-art allocation methods, three approaches were considered: the RMLSA-OFC method [19], the First Fit (FF) algorithm, and the Random Wavelength Assignment (RWA) algorithm [20,21]. The method in [19] employs a heuristic algorithm for allocation using optical frequency combs (OFCs). In contrast, the FF method sequentially assigns resources by selecting the first available carrier that meets the bandwidth requirement, while the RWA method allocates wavelengths in a random manner, ensuring that each selected wavelength satisfies the transmission requirements. \nFigure 6 demonstrates that the method proposed in [19] can effectively allocate up to 110 requests with a low BBR, reaching a maximum value of 1.5. This indicates a lower performance compared to our method (see Figure 5). The ellipses in Figure 6 highlight regions with the highest BBR values, marking critical performance areas. A dashed line indicates the threshold at approximately 110 requests, beyond which the allocation method's performance declines as the number of requests increases. This visual representation emphasizes the system's limitations under higher demand. In contrast, our approach maintains effective allocation up to 170 requests, showing a clear difference of 60 clients. \nWhen comparing the results of our RMLSA-ILP-OFC approach to those of the FF method (see Figure 7), a marked increase in the Blocking-to-Bandwidth Ratio (BBR) is observed, with rejections exceeding 1 in several instances (marked in yellow and light blue). The BBR values, ranging from 1.5 to 3.0 (highlighted with red ellipses), indicate critical points that significantly affect Quality of Service (QoS). Additionally, the allocation method begins to fail at approximately 105 requests (red dotted line), leading to a sharp rise in BBR. These findings underscore the limitations of the FF method, which struggles to manage bandwidth efficiently under high-demand scenarios, highlighting the need for more robust solutions. Our approach demonstrates its superiority by maintaining resource allocations effectively up to 170 requests."
]
embeddings = model.encode(sentences)
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [4, 4] 
